Problem 273

Sum of Squares

Consider equations of the form: `a`^{2} + `b`^{2} = `N`, 0 `a` `b`, `a`, `b` and `N` integer.

For `N`=65 there are two solutions:

`a`=1, `b`=8 and `a`=4, `b`=7.

We call S(`N`) the sum of the values of `a` of all solutions of `a`^{2} + `b`^{2} = `N`, 0 `a` `b`, `a`, `b` and `N` integer.

Thus S(65) = 1 + 4 = 5.

Find S(`N`), for all squarefree `N` only divisible by primes of the form 4`k`+1 with 4`k`+1 150.

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